BuddyPress.org

WP Mail SMTP seems to be a well-written plugin. I’ve taken a quick look at its code, and how it affects what WordPress does, and it looks like BuddyPress – in theory – should work with it. However, if you say it doesn’t, I don’t know why – you’d have to spend time debugging what is going on.

If you know some PHP and basic WordPress development, I can give you some pointers (e.g. start looking at the phpmailer_init hooks and how both plugins add to it).